Ehlers Transformations and String Effective Action

Abstract

We explicitly obtain the generalization of the Ehlers transformation for stationary axisymmetric Einstein equations to string theory. This is accomplished by finding the twist potential corresponding to the moduli fields in the effective two dimensional theory. Twist potential and symmetric moduli are shown to transform under an $O(d,d)$ which is a manifest symmetry of the equations of motion. The non-trivial action of this $O(d,d)$ is given by the Ehlers transformation and belongs to the set $\frac{O(d)\times O(d)}{O(d)}$.

13 pages, minor corrections, version to appear in Physics Letters B358

References in corpus (4)

• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Duality Symmetries of 4D Heterotic Strings
• O(2,2) Transformations and the String Geroch Group
• "Separation of Variables and Hamiltonian Formulation for the Ernst Equation"

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• String theory extensions of Einstein-Maxwell fields: the static case
• O(d,d)-Duality in String Theory
• Integrability of generalized (matrix) Ernst equations in string theory
• Field Theoretical Quantum Effects on the Kerr Geometry
• Boosting some type--D metrics